A refined equivalent single-layer model of geometrically non-linear doubly curved layered shells using mixed variational approach

An extension of Reissner's mixed variational formula is presented based on Maupertuis' principle for geometrically non-linear elastic composite laminated structures. Legendre's transformation is used to introduce in the variational statement the complementary energy density as a function of stresses only. A refined equivalent single-layer model of doubly curved shells is established using the resulting mixed variational formula. The present single-layer shell model accounts for the basic displacement assumptions of the first-order shear deformation theory, and stresses that are continuous through the shell thickness and consistent with the surface conditions. Therefore, the present first-order shell model does not require any of the shear correction factors used in other first-order theories, and it recovers the interlaminar stresses without losing its simplicity. The present model can be easily specialized to flat plates, cylindrical and spherical shells. (C) 2000 Elsevier Science Ltd. All rights reserved.